With advances in data acquisition methods and technical platforms, omics measurement collection yields increasingly complex data structures. While high-dimensional matrices with more variables than samples can be handled via multivariate methods, extracting information is more challenging in the case of experimental designs involving several factors. Multifactorial models combining ANOVA and multivariate approaches have been developed for this purpose, but analyzing unbalanced designs remains challenging, especially when several data blocks are integrated.

This study introduces integrative AComDim (iAComDim) and integrativeAMOPLS (iAMOPLS) for the analysis of multifactorial data from multiple sources. These methods implement a rebalancing strategy tailored for multiblock settings, ensuring unbiased effect estimators and orthogonal effect matrices even with unbalanced designs. When applied to a multiomics benchmark dataset with two experimental factors, these approaches effectively separate the sources of variation related to the effects in the design while summarizing information into a single multiblock model. Rebalancing strategies prevent the mixing of variation sources in extracted components, and their integration with multiblock chemometric methods offers an efficient and versatile solution for analyzing complex data structures.

This work establishes a novel framework for analyzing data from single or multiple sources within multifactorial experimental designs. Furthermore, the proposed methods are flexible enough to analyze unbalanced designs with heterogeneously missing replicates across multiple tables, making them broadly applicable for handling multiomics or other datasets in various application domains.